Topological data analysis (TDA) is non-parametric approach to data analysis that looks for topological features, like connected components, loops and cavities. Since the seminal work of [1]}, TDA has been used for a wide range of applications (for instance [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, see also the references therein). Such features, called homology, are coordinate-free and hence invariant under a wide range of transformations like rotation, translation, scaling and stretching. For instance, the dataset in fig:TDAillustrationwavycircle, consisting of points sampled near a wavy circle, form one loop (when appropriately connected), just like points sampled near the unit circle.
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